Question

Solve the equation if possible. Does the equation have one solution, is it an identity, or does it have no solution? $$ 12-2 a=-5 a-9 $$

Short answer

The solution to the equation is a = -1, and the equation has one solution.

Step-by-step solution

Bring like terms together

In order to simplify the equation, bring like terms together. This will lead to \( 12 + 5a = 2a + 9 \).

Isolate Variable 'a'

Continue to simplify the equation by isolating the variable 'a'. By subtracting '2a' from both sides of the equation, we will get \( 3a = -3 \).

Solve for 'a'

To solve for 'a', divide both sides of the equation by '3' which results in \( a = -1 \).

Substitute 'a' back into the initial equation

Finally, substitute 'a' back into the initial equation to confirm whether it balances. The initial equation was \( 12 - 2a = -5a - 9 \). If we substitute 'a = -1' into this equation, it will balance, confirming that the equation has one solution.